A comparison of two closely-related approaches to aerodynamic design optimization

Two related methods for aerodynamic design optimization are compared. The methods, called the implicit gradient approach and the variational (or optimal control) approach, both attempt to obtain gradients necessary for numerical optimization at a cost significantly less than that of the usual black-box approach that employs finite difference gradients. While the two methods are seemingly quite different, they are shown to differ (essentially) in that the order of discretizing the continuous problem, and of applying calculus, is interchanged. Under certain circumstances, the two methods turn out to be identical. We explore the relationship between these methods by applying them to a model problem for duct flow that has many features in common with transonic flow over an airfoil. We find that the gradients computed by the variational method can sometimes be sufficiently inaccurate to cause the optimization to fail

Lifshitz fermionic theories with z=2 anisotropic scaling

We construct fermionic Lagrangians with anisotropic scaling z=2, the natural counterpart of the usual z=2 Lifshitz field theories for scalar fields. We analyze the issue of chiral symmetry, construct the Noether axial currents and discuss the chiral anomaly giving explicit results for two-dimensional case. We also exploit the connection between detailed balance and the dynamics of Lifshitz theories to find different z=2 fermionic Lagrangians and construct their supersymmetric extensions.Comment: Typos corrected, comment adde

On Eigenvalue spacings for the 1-D Anderson model with singular site distribution

We study eigenvalue spacings and local eigenvalue statistics for 1D lattice Schrodinger operators with Holder regular potential, obtaining a version of Minami's inequality and Poisson statistics for the local eigenvalue spacings. The main additional new input are regular properties of the Furstenberg measures and the density of states obtained in some of the author's earlier work.Comment: 13 page

Taking Stock of Common Core Math Implementation: Supporting Teachers to Shift Instruction: Insights from the Math in Common 2015 Baseline Survey of Teachers and Administrators

In spring 2015, WestEd administered surveys to understand the perspectives on Common Core State Standards-Mathematics (CCSS-M) implementation of teachers and administrators in eight California school districts participating in the Math in Common (MiC) initiative. From this survey effort, we were able to learn from over 1,000 respondents about some of the initial successes and challenges facing California educators attempting to put in place and support new -- and what some consider revolutionary -- ideas in U.S. mathematics education

On the Fredholm property of bisingular pseudodifferential operators

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the equivalence of their ellipticity (defined by the invertibility of certain associated homogeneous principal symbols) and their Fredholm mapping property in associated scales of Sobolev spaces. We also prove the spectral invariance of these operator classes and then extend these results to the even larger classes of Toeplitz type operators.Comment: 21 pages. Expanded sections 3 and 4. Corrected typos. Added reference

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the representation is of determinant class we prove, generalizing the Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister torsions are equal.Comment: 78 pages, AMSTe

Conormal distributions in the Shubin calculus of pseudodifferential operators

We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms and microlocal properties.Comment: 23 page

Longitudinal effect in the dependence of the critical frequency of the midlatitude E layer on solar activity

Variations in the critical frequency of the E layer, foE, measured at Boulder and Tashkent stations located at almost coinciding geographical latitudes but at strongly different geomagnetic latitudes are analyzed. The following conclusions are drawn. (a) Late in the fall and in the winter, the foE values at these stations are distinctly different at low solar activity. This difference decreases with increasing solar activity. In other words, the longitudinal effect in the foE dependence on solar activity is significant for these conditions. (b) This effect is almost absent in summer; i.e., the difference in foE dependence on solar activity at these stations is insignificant for the given season. It has been substantiated that the dependence of the nitric oxide concentration [NO] on geomagnetic latitude, season, and solar activity is one of the main causes of this longitudinal effect. © Pleiades Publishing, Ltd. 2007

Properties of the F2-layer critical frequency median in the nocturnal subauroral ionosphere during low and moderate solar activity

© 2016, Pleiades Publishing, Ltd.Based on an analysis of data from the European ionospheric stations at subauroral latitudes, it has been found that the main ionospheric trough (MIT) is not characteristic for the monthly median of the F2-layer critical frequency (foF2), at least for low and moderate solar activity. In order to explain this effect, the properties of foF2 in the nocturnal subauroral ionosphere have been additionally studied for low geomagnetic activity, when the MIT localization is known quite reliably. It has been found that at low and moderate solar activity during night hours in winter, the foF2 data from ionospheric stations are often absent in the MIT area. For this reason, a model of the foF2 monthly median, which was constructed from the remaining data of these stations, contains no MIT or a very weakly pronounced MIT